Constraints on the slope of the dark halo mass function by microlensing observables^*

¹ Dipartimento di Fisica E.R. Caianiello, Università di Salerno, Via S. Allende, 84081 Baronissi (Salerno), Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia, Edificio G, 80126 Napoli, Italy
³ Dipartimento di Scienze Fisiche, Università di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia, Edificio N, 80126 Napoli, Italy
⁴ Osservatorio Astronomico di Capodimonte, Via Moiariello 16-80131 Napoli, Italy

Corresponding author: V. F. Cardone, Vincenzo.Cardone@na.infn.it

Accepted: 17 May 2001

Abstract

We investigate the dark halo lens mass function (MF) for a wide class of spheroidal non singular isothermal models comparing observed and observable microlensing quantities for MACHO observations towards LMC and taking into account the detection efficiency. We evaluate the microlensing observable quantities, i.e. observable optical depth, number of events and mean duration, for models with homogenous power-law MF changing the upper and lower mass limits and the flattening of the dark halo. By applying the simple technique of the inverse problem method we are then able to get some interesting constraints on the slope α of the MF and on the dark halo mass fraction f made out by MACHOs consistently with previous results.